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<table width="100%" summary="page for selenium"><tr><td>selenium</td><td style="text-align: right;">R Documentation</td></tr></table>

<h2>
Data from toxicology experiments with selenium
</h2>

<h3>Description</h3>

<p>Comparison of toxicity of four types of selenium by means of dose-response analysis
</p>


<h3>Usage</h3>

<pre>data(selenium)</pre>


<h3>Format</h3>

<p>A data frame with 25 observations on the following 4 variables.
</p>

<dl>
<dt><code>type</code></dt><dd><p>a numeric vector indicating the form of selenium applied</p>
</dd>
<dt><code>conc</code></dt><dd><p>a numeric vector of (total) selenium concentrations</p>
</dd>
<dt><code>total</code></dt><dd><p>a numeric vector containing the total number of flies</p>
</dd>
<dt><code>dead</code></dt><dd><p>a numeric vector containing the number of dead flies</p>
</dd>
</dl>



<h3>Details</h3>

<p>The experiment is described in more details by Jeske et al. (2009).
</p>


<h3>Source</h3>

<p>Jeske, D. R., Xu, H. K., Blessinger, T., Jensen, P. and Trumble, J. (2009) Testing for the Equality of EC50 Values in the Presence of 
Unequal Slopes With Application to Toxicity of Selenium Types, <em>Journal of Agricultural, Biological, and Environmental Statistics</em>,
<b>14</b>, 469&ndash;483</p>


<h3>Examples</h3>

<pre>

## Analysis similar to what is proposed in Jeske et al (2009)
##  but simply using existing functionality in "drc"

## Fitting the two-parameter log-logistic model with unequal ED50 and slope
sel.m1 &lt;- drm(dead/total~conc, type, weights=total, data=selenium, fct=LL.2(), 
type="binomial")
#sel.m1b &lt;- drm(dead/total~conc, type, weights=total, data=selenium, fct=LN.2(), 
# type="binomial", start=c(1,1,1,1,50,50,50,50))
plot(sel.m1, ylim = c(0, 1.3))
summary(sel.m1)

## Testing for equality of slopes
sel.m2 &lt;- drm(dead/total~conc, type, weights=total, data=selenium, fct=LL.2(), 
type="binomial", pmodels=list(~1, ~factor(type)-1))
sel.m2b &lt;- drm(dead/total~conc, type, weights=total, data=selenium, fct=LN.2(), 
type="binomial", pmodels=list(~1, ~factor(type)-1))
plot(sel.m2, ylim = c(0, 1.3))
summary(sel.m2)
anova(sel.m2, sel.m1)  # 48.654
#anova(sel.m2b, sel.m1b)
# close to the value 48.46 reported in the paper

## Testing for equality of ED50
sel.m3&lt;-drm(dead/total~conc, type, weights=total, data=selenium, fct=LL.2(), 
type="binomial", pmodels=list(~factor(type)-1, ~1))
#sel.m3b&lt;-drm(dead/total~conc, type, weights=total, data=selenium, fct=LN.2(), 
# type="binomial", pmodels=list(~factor(type)-1, ~1), start=c(1,1,1,1,50))
plot(sel.m3, ylim = c(0, 1.3))
summary(sel.m3)

anova(sel.m3, sel.m1)  # 123.56
#anova(sel.m3b, sel.m1b) 
# not too far from the value 138.45 reported in the paper
# (note that the estimation procedure is not exactly the same)
# (and we use the log-logistic model instead of the log-normal model)

</pre>


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